Interesting question. Unfortunately, there aren't really any easy answers to this - there are a million ways to do anything in Flash, and depending on what the original developer did you have various things you can try.
The Flash Player provides an ExternalInterface method right in the native API, so every Flash application CAN call javascript. If the developer configured it, you can even register an internal callback method in flash to respond to javascript commands - so you can get it working both ways.
That said, unless the developer specifically put that in because you wanted it it's unlikely he did it, and there'd be no way for you to see it anyway.
Depending on how the swf is built, there are a couple of options that you have. First and foremost, you can try adding the LOOP=TRUE parameter to your embed code (more info here). If this is a basic timeline animation, or if the frames of your video clip have been dumped onto the timeline and it's using Flash's own animation tools to play it then this might be all you need.
If that doesn't work, though, things get a bit more complex. You could try to decompile the .swf using one of any number of Flash decompilers - that might give you some insight into what methods are there, how it's structured, etc. It's not exactly a fine science, though - you're in for some trial and error.
If in the process of introspecting the swf you learn, for instance, that it has an object called "video" of type "Video" then you can write a wrapper .swf, load in your target swf and have your wrapper interface with JavaScript. If all you're looking for is a loop, the video object might even have an autorepeat property or something to that effect.
That was a bit long winded, but I hope it helped. Leave a comment if you have any questions!